Equal Probabilities

I have a question about quantum mechanics. I was reading up on probability fields and it occurred to me that if there is a possibility that a subatomic particle may exist in a very unusual place like say jumping from Utah to Ohio in any give frame of time that has yet to happen and you can divide any give portion of time into an infinite number of frames. Does this mean that there are an infinite number of changes for that particle to be in any location and does this mean that the probabilities are equal?
In addition I would like to ask the question if physics equations can make no distinction between past and future does this mean that it is also a mater of guess work where things were?
Note: I still don’t understand the equations yet so please put in lays-man terms.

If you make really "pure" calculations, where you include some nice potential and only one particle, then yes, you find that situations like this can occur.

But the biggest mistake you make there is that you actually make a way too many simplified assumptions. Fact is you don't have just one particle, or some smooth potential. The environment is so full of "junk" which will disrupt your system continiously, that stuff like tunneling over 1000 miles simply can not happen.The keyword here is decoherence.

How exactly do you think decoherence prohibits or affects tunneling over large distances?

In any experiment the total probability of detecting such an event would already, by definition, be immeasurably close to zero.. so I really see no call to suggest additional mechanisms of avoiding it outright.

But the point was that it could happen an infinite number of times in one second doesn't this raise the probability so that no matter how close to zero it is in one frame that it is extremly of probable. I mean I know tunnling that far in extremly improbable but i was just confused because if you do something an infinite number of times un less it is infinitely imporbable

But the point was that it could happen an infinite number of times in one second doesn't this raise the probability so that no matter how close to zero it is in one frame that it is extremly of probable. I mean I know tunnling that far in extremly improbable but i was just confused because if you do something an infinite number of times un less it is infinitely imporbable

something like that would only be possible IF there were an infinite number of divisions/events per unit of time- but QM shows us that time is not continuous- it is quantized and the smallest instant of time that has any physical meaning is the Planck Time: 10^-44 sec- the probability of a particle tunneling to Andromeda [or Ohio] is so remote that with only 10^44 'changes'- as you say- per second- it would still take googolplexes of gigayears before such an event would be observed- however that doesn't mean that such an event could not be technologically harnessed- it may be possible to artificially manipulate a particle so that this remote probability becomes a certainty- quantum computers are an example of that sort of idea